On September 19, 1863, Burnham was overseeing the artillery on Lookout Mountain at the Battle of Chickamauga. With Confederate troops charging his position, he attempted to bring his horses forward to haul off the guns, but alert Confederates shot the animals as soon as they were within sight.[4] With no chance of escape, he ordered his gunners to load their four 12-pound Napoleons with double-shotted canister.[4] Battery H opened up as soon as the 18th Infantry skirmishers were clear, causing the Confederates to take cover.[4] The 16th Infantrymen in front of the guns occupied a slightly lower elevation and saw the shells flying over their heads.[4] But Battery H did not have much infantry support and enemy fire quickly shot down their gunners.[4] Burnham was shot in the chest, fatally wounded.[4] When his second in command, Lt. Joshua A. Fessenden, asked Burnham if he was hurt, he responded: "Not much, but save the guns!"[4].

Lt. Fessenden had the following to say about the battle that day:"During the morning, after an all night march, we were ordered forward by General King. The battery was hardly in position before the troops on the right gave way and it was exposed to a most terrific fire of musketry from front and flank. General King ordered us to limber to the rear, but it was impossible to execute the order, since many of the cannoneers were either killed or wounded, and the horses shot at the limbers. At the first fire, Lieut. Burnham fell mortally wounded; Lieut. Ludlow was also wounded and fell into the enemy's hands, and myself slightly wounded in the side. The battery was taken by the enemy, after firing sixteen rounds of canister."[6]

Lt. Fessenden had himself been shot in the hip, but he assumed command.[6] Battery H was overrun but Lt. Fessenden successfully rallied his troops, recaptured his artillery, and even took one gun of the Confederates.[6] Lt. Fessenden kept the field and brought off the pieces but without their caissons as these had to be abandoned through lack of horses.[6] While the battle ranged on Burnham survived for another two hours.[3] In addition to Burnham, 42 men in his unit were either killed or wounded and more than one-third of the horses were shot that day.[3][7]

Gen. John King dispatched the following in his report:"I take this occasion to speak in the highest terms of the officers of Battery H, 5th Artillery, 1st Lieut. H. M. Burnham and 2d Lieutenants Israel Ludlow and J. A. Fessenden. The officers of this battery, finding it impossible to retire, remained with their pieces, firing, until they were forcibly taken from them by the enemy."[6]

↑ 10.010.110.2Burnham, Roderick Henry (1884). Genealogical Records of Thomas Burnham, the Emigrant, who was Among the Early Settlers at Hartford, Connecticut, U.S. America, and His Descendants. Hartford, CT: Case, Lockwood & Brainard Co..

Burnham, Roderick Henry (1884). Genealogical Records of Thomas Burnham, the Emigrant, who was Among the Early Settlers at Hartford, Connecticut, U.S. America, and His Descendants. Hartford, CT: Case, Lockwood & Brainard Co.. ISBN111219164X.